If you use an Amex or Visa card to buy your travel and you are enrolled in their respective rewards program and also have a FF card, then not only do you get the flying points but you can then transfer the points accrued in the rewards program to the FF program.
I think I read somewhere else that even transferring credit card amounts to other cards allows a 'double dip' between the two card reward programs.

Personally, I use the cards points to buy things for the rest of the family. This is to make up (read 'bribe') for all the time I spend travelling.